The soundboard is exposed all the time, so dust settles on it and collects especially between the bridges. Routine cleaning is therefore worthwhile.
Use a soft brush and work gently along the grain. Brushes that are too stiff can scratch the surface and leave marks of their own.
Do not wipe the soundboard with a damp cloth over a large area. Absorbed moisture makes the soundboard heavier, which directly affects how it transmits vibration; the tone turns dull and takes a long time to recover.
Nor should wax polish be used on the soundboard. It makes the surface slippery, reduces friction under the bridges and lets them shift or jump.
The rims and sides can be wiped with a clean soft cloth. For stubborn marks, ask a professional before trying anything — solvents can damage the finish.